Correlation induced localization of lattice trapped bosons coupled to a Bose-Einstein condensate

TL;DR

This paper explores how correlations in a two-species bosonic system cause localization of lattice-trapped atoms, using advanced computational methods and effective Hamiltonian models to analyze the transition from uncorrelated to correlated states.

Contribution

It provides a detailed analysis of correlation-induced localization in a coupled bosonic system, employing ML-MCTDHX and effective Hamiltonian approaches beyond mean-field theory.

Findings

Wave function transitions from uncorrelated to correlated states with increased lattice depth and interaction.

Identification of a process responsible for the localization crossover in a single-particle picture.

Development of an order parameter as an experimental signature of the transition.

Abstract

We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb-Liniger type gas. Our main goal is the description and in depth exploration and analysis of the two-species many-body quantum system including all relevant correlations beyond the standard mean-field approach. To achieve this, we use the Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in the localization of the lattice atoms in the latter regime. For small interspecies couplings, we identify the process responsible for this cross-over in a single-particle-like picture. Moreover, we give a full characterization of the wave function's structure in both regimes, using Bloch and Wannier states of the lowest band, and we find an order parameter, which can be exploited as a corresponding experimental signature. To deepen the understanding, we use an effective Hamiltonian approach, which introduces an induced interaction and is valid for small interspecies interaction. We finally compare the ansatz of the effective Hamiltonian with the results of the ML-MCTDHX simulations.